Models Of Field Aligned Currents Needful To Simulate The Substorm ...

Ann. Geophysicae 14, 1356—1361 (1996)
EGS — Springer-Verlag 1996
Models of ﬁeld-aligned currents needful to simulate
the substorm variations of the electric ﬁeld
and other parameters observed by EISCAT
M. A. Volkov, A. A. Namgaladze
Polar Geophysical Institute, 15 Halturina St., Murmansk, 183010, Russia
Murmansk State Technical University, 2 Sportivnaya St., Murmansk, 183010, Russia
Received: 24 January 1996/Revised: 27 May 1996/Accepted: 29 May 1996
Abstract. We have used the global numerical model of the
sphere-protonosphere system (Namgaladze et al., 1988,
coupled ionosphere-thermosphere-protonosphere system
1991) has been used to calculate the variations in electric
to simulate the electric-ﬁeld, ion- and electron-temper-
ﬁeld and ion and electron temperature and con-
ature and -concentration variations observed by EISCAT
centration for the quiet day of 24 March 1987 and
during the substorm event of 25 March 1987. In our
disturbed day of 25 March. The model input data for
previous studies we adopted the model input data for
ﬁeld-aligned currents and precipitating electron ﬂuxes
ﬁeld-aligned currents and precipitating electron ﬂuxes to
have been selected to obtain an acceptable agreement
obtain an agreement between observed and modelled
between variations observed by EISCAT (Collis and Ha¨g-
ionospheric variations. Now, we have calculated the ﬁeld-
gstro¨m, 1989, 1991) and those from the ionospheric
aligned currents needful to simulate the substrom vari-
modes. The best agreement has been achieved when the
ations of the electric ﬁeld and other parameters observed
ﬁeld-aligned currents of the substorm current wedge were
by EISCAT. The calculations of the ﬁeld-aligned currents
added to the region-1 and 2-ﬁeld-aligned currents during
have been performed by means of numerical integration of
an active phase of a substorm.
the time-dependent continuity equation for the cold mag-
The three-dimensional current system, named the sub-
netospheric electrons. This equation was added to the
storm current wedge, has been suggested and discussed by
system of the modelling equations including the equation
many authors (e.g. Bonnevier et al., 1970; McPherron
for the electric-ﬁeld potential to be solved jointly. In this
et al., 1973; Kamide et al., 1976; Rothwell et al., 1984;
case the inputs of the model are the spatial and time
Rostoker and Eastman, 1987; Kan et al., 1988, 1992; Kan,
variations of the electric-ﬁeld potential at the polar-cap
1993). It consists of the ﬁeld-aligned currents ﬂowing out
boundaries and those of the cold magnetospheric electron
of the ionosphere at the pre-midnight sector and ﬂowing
concentration which have been adopted to obtain the
in at the post-midnight sector closed by the horizontal
agreement between the observed and modelled ionos-
ionospheric currents and magnetospheric currents per-
pheric variations for the substorm event of 25 March
pendicular to the geomagnetic ﬁeld. In Namgaladze et al.
1987. By this means it has been found that during the
(1996) the spatial and time variations of such a ﬁeld-
active phase of the substorm the current wedge is formed.
aligned current system were not calculated but selected to
It is connected with the region of the decreased cold
obtain the best ﬁt to the electric-ﬁeld variations observed
magnetospheric electron content travelling westwards
by EISCAT.
with a velocity of about 1 km s\ at ionospheric levels.
In the present paper an attempt is made to calculate the
ﬁeld-aligned currents of region 2 and those of the sub-
storm current wedge for the same event of 25 March 1987
rather than selecting them. In this case the ﬁeld-aligned
currents are transferred from the category of input para-
1 Introduction
meters for the model to the category of calculated para-
meters. Simultaneously, new input parameters, namely
The behaviour of the high-latitude ionosphere during an
electric-ﬁeld potential at the polar-cap boundaries and
isolated substorm observed on 25 March 1987 has been
equivalent magnetospheric conductivity, are introduced
simulated numerically by Namgaladze et al. (1996). The
and variations of these parameters are selected to obtain
global numerical model of the Earth’s thermosphere-iono-
the best agreement between EISCAT-observed and
modelled ionospheric variations. In this way we attempt
to answer the question: what magnetospheric conductiv-
Correspondence to: A. A. Namgaladze
ity variations can be responsible for the formation of the

M. A. Volkov, A. A. Namgaladze: Models of ﬁeld-aligned currents needful to simulate the substorm variations of the electric ﬁeld
1357
substorm current wedge and for the corresponding iono-
Eq. 1 has been obtained by Vasyliunas (1972) and Maltsev
spheric variations of the electric ﬁeld and electron and ion
(1974). In our calculations the ﬁeld-aligned currents are
temperature and concentration? As it will be shown, the
assumed to be ﬂowing only at the closed dipole geomag-
development of the current wedge during the substorm
netic ﬁeld lines up to the polar-cap boundary, along which
active phase can be related to the region of the decreased
the distribution of the electric-ﬁeld potential is taken in
cold magnetospheric electron content travelling west-
the following form:
wards with a velocity of about 1 km s\ at ionospheric
levels.
@"[ A(t)/2] sin ,
(3)
where
A is the potential drop across the polar cap. Its
variation during the growth phase of the substorm
2 Formulation of the problem, basic equations
(1540—1640 UT) is taken as the linear increase from 20 to
80 kV. The variations of the precipitating electron ﬂuxes
The model calculations of the variations in ionospheric
are taken in the same form as in Namgaladze et al. (1996).
electric ﬁeld and electron and ion temperature and con-
The integrated magnetospheric conductivity distribu-
centration for the substorm event of 25 March 1987 have
tion during the quiet conditions till up to the moment of
been performed using the new version (Namgaladze et al.,
the beginning of the growth phase (1540 UT) is taken in
1995a) of the global numerical model of the Earth’s
the form:
thermosphere-ionosphere-protonosphere system (Nam-
galadze et al., 1988, 1994) analogous to the calculations
K" exp [!( ! @)/( )],
5 @"16°,
(4)
made by Namgaladze et al. (1996). The main diﬀerence is
where @ is the geomagnetic colatitude of the polar-cap
that now the ﬁeld-aligned currents are not the input
boundary,
"10°,
"100 Sm. During the growth
parameters for the model, but have been calculated by
phase of the substorm (1540—1640 UT), the polar-cap
solving the time-dependent continuity equation for the
boundary moves linearly 4° equatorwards.
cold magnetospheric plasma-sheet electrons integrated
The expansion phase of the substorm continues for
along the closed geomagnetic ﬁeld lines:
20 min (1640—1700 UT). During this phase the integrated
magnetospheric conductivity varies by the following
jN"!BG* K/*t!R\
# sin\ [(* K/* ) (* /* )
means:
!(* K/* ) (* /* )],
(1)
K" K+1!0.3 exp [!( ! (t))/( )],,
(5)
where jN is the ﬁeld-aligned current density deﬁned to be
where
"23° is the longitudinal half-width of the re-
positive for currents ﬂowing out the ionosphere; BG is the
gion of the decreased plasma-sheet electron content cen-
geomagnetic ﬁeld at the base of the ﬁeld line in the
tred at the longitude
ionosphere (h
. The centre of the region is moving
"175 km);
K"eN/BG is the integrated
westwards with a speed of 1.2 km s\ at the ionosphere
pseudo-Hall magnetospheric conductivity; e"the elec-
level. The maximum decrease in the plasma-sheet electron
tron charge; N"BG(n/B)dl, where the integration is car-
content, and correspondingly in the integrated magneto-
ried out along geomagnetic ﬁeld lines from h"175 km up
spheric conductivity, is 30%. Figure 1 shows the northern
to the top of the ﬁeld line, n is the concentration of the
polar geomagnetic ( ,
) plot of the integrated magneto-
magnetospheric plasma-sheet electrons, and so N is half of
spheric conductivity at 1550 UT (top panel) and 1650 UT
the total plasma-sheet electron content in the ﬁeld line
(bottom panel).
tube; t is time; R# is the Earth’s radius; is the geomag-
During the recovery phase of the substorm (after
netic colatitude,
is the geomagnetic longitude measured
1700 UT), the distributions of the magnetospheric con-
from magnetic midnight to east;
is the electric-ﬁeld
ductivity and electric-ﬁeld potential at the polar-cap
potential determined from the continuity equation for the
boundary recover to the undisturbed state exponentially,
ionospheric currents:
with the characteristic time of 1.5 h.

Equations 1 and 2 were solved numerically together
[ L G( !;B)!jN]"0.
(2)
with all other equations of the model, namely the continu-
Here L G is the ionospheric conductivity tensor, is the
ity, momentum and heat balance equations for the main
neutral wind velocity vector. Both are calculated in the
neutral gases (N, O, O), molecular (O> and NO>) and
model by solving the continuity and momentum equa-
atomic (O> and H>) ions, and electrons for the height
tions for the neutral and charged particles. B and jN are the
range of 80 km up to 15 R# geocentric distance. The
vectors of the geomagnetic ﬁeld and ﬁeld-aligned current
detailed description of the model equations can be found
density, respectively.
in Namgaladze et al. (1988). In our new version of this
Equation 1 is obtained from the time-dependent conti-
model (Namgaladze et al., 1995a) we use the variable
nuity equation for the magnetospheric plasma-sheet elec-
latitudinal steps of numerical integration. They vary from
trons under the following assumptions. The ﬁeld-aligned
10° for the thermospheric parameters and 5° for the iono-
currents are carried by the electrons; the magnetospheric
spheric F2-region and protonosphere parameters at the
plasma-sheet electrons are cold, i.e. their gradient and
equator to 2° at the auroral zones for all parameters. In
other drifts are neglected in comparison with the electro-
Namgaladze et al. (1996) we used the empirical MSIS-86
magnetic one; the electric ﬁeld is potential. The geomag-
(Hedin, 1987) thermospheric model to calculate the tem-
netic ﬁeld lines are electrically equipotential; n is constant
perature and composition of the thermosphere. In the
along the geomagnetic ﬁeld lines. For the stationary case
present paper all calculations are self-consistent. It means

1358
M. A. Volkov, A. A. Namgaladze: Models of ﬁeld-aligned currents needful to simulate the substorm variations of the electric ﬁeld
Fig. 1. The north geomagnetic ( ,
) polar plots of the integrated
Fig. 2. The geomagnetic ( ,
) polar plots of the calculated electric-
magnetospheric conductivity (Sm) at the growth phase (top) and at
ﬁeld potential (kV) in the northern high-latitude ionosphere at the
the expansion phase (bottom) of the substorm; the Sun position is at
growth phase (top) and at the expansion phase (bottom) of the
the top of the ﬁgure
substorm; the Sun position is at the top of the ﬁgure
that the full system of the modelling equations for the
wedge) appears at the midnight sector. It is produced by
neutral and charged particles is solved. The diﬀerences
the westward-travelling region of the decreased magneto-
between the self-consistent solutions and those obtained
spheric conductivity. The outﬂowing current is westward
by the use of the MSIS-86 model were discussed by
from the inﬂowing. The maximum density of the out-
Namgaladze et al. (1995b). These diﬀerences are signiﬁ-
ﬂowing current is about 1 A m\. In the case when the
cant for the calculated thermospheric wind disturbances
region of the decreased magnetospheric conductivity is
but are not important for the calculated ﬁeld-aligned
not travelling, the current-wedge ﬁeld-aligned currents are
current and electric-ﬁeld variations discussed here.
generated by !V#· N in magnetospheric plasma, where
V# is E; B plasma drift. Therefore they are generated at
the eastern and western edges of the region of decreased
3 The results of the model calculations
plasma content as far as V# is eastward in the region of
decreased plasma content. We can see that it is really so in
The calculated electric-ﬁeld potential and ﬁeld-aligned
the midnight sector in our calculations when comparing
currents at the northern high-latitude ionosphere for the
Figs. 1, 2 and 3 (bottom panels).
diﬀerent phases of the substorm are shown in Figs. 2 and 3.
An inﬂuence of the westward travelling of the region of
The ﬁeld-aligned currents of region 1 are distributed along
the decreased magnetospheric conductivity on the cal-
the polar-cap boundary and are not shown in Fig. 3.
culated ﬁeld-aligned current density is illustrated in Fig. 4.
During the quiet conditions and growth phase of the
It shows the longitudinal variations of the ﬁeld-aligned
substorm, the calculated electric-ﬁeld potential and ﬁeld-
current density along the geomagnetic latitude 68° cal-
aligned currents are consistent with the average statistical
culated for the cases when the region of the decreased
picture of these parameters for the weakly disturbed
magnetospheric conductivity is travelling westwards and
geomagnetic conditions (Heppner and Maynard, 1987;
when it is motionless. In the last case the ﬁeld-aligned
Iijima and Potemra, 1978). During the expansion phase of
current density is noticeably less than in the case of
the substorm a pair of the ﬁeld-aligned currents ﬂowing
the travelling region. Correspondingly, the electric ﬁeld in
out of and into the ionosphere (the substorm current
the midnight sector is decreased. The inﬂuence of the

M. A. Volkov, A. A. Namgaladze: Models of ﬁeld-aligned currents needful to simulate the substorm variations of the electric ﬁeld
1359
Fig. 3. The geomagnetic ( ,
) polar plots of the calculated ﬁeld-
Fig. 5. The calculated variations (solid curves) and those observed
aligned current density (A km\) in the northern high-latitude iono-
by EISCAT on 25 March 1987 (dashed curves) in the north-
sphere at the growth phase (top) and at the expansion phase (bottom)
ward electric ﬁeld (bottom panel ), E-region electron concentration at
of the substorm; the Sun position is at the top of the ﬁgure
111-km altitude and F2-region ion and electron temperature and
electron concentration at 279-km altitude
111 and 279 km, and electron and ion temperature at the
279-km altitude over the EISCAT transmitter position are
shown in Fig. 5 together with the variations of these
parameters observed by EISCAT on 25 March 1987 (Col-
lis and Ha¨ggstro¨m, 1989, 1991). As can be seen in this
ﬁgure, the agreement between the observed and calculated
variations is quite satisfactory.
4 Discussion of the results
The presented results show that the behaviour of the
electric ﬁeld, electron concentration and electron and ion
Fig. 4. The calculated longitudinal variations of the ﬁeld-aligned
temperature observed by EISCAT during the isolated
current density along the 68° geomagnetic latitude in the end of the
substorm on 25 March 1987 can be satisfactorily
substorm expansion phase for the cases: 1, the region of decreased
simulated in the numerical model calculations assuming
magnetospheric conductivity is travelling westwards and 2, it is at
rest
the appearance of the westward-travelling region of the
decreased plasma-sheet electron content during the ex-
pansion phase of the substorm. Due to the appearance of
travelling speed VRP of the decreased plamsa content region
this region, the substorm current wedge is formed in
on the current wedge ﬁeld-aligned current generation is
accordance with the ideas of Bonnevier et al. (1970),
opposite that of V#: the westward travelling of the ‘‘hole’’
McPherron et al. (1973), Kamide et al. (1976) and others,
acts as the eastward electromagnetic plasma drift.
and with the observations of the ﬁeld-aligned currents
The calculated time variations of the northward elec-
during the substorm expansion phase (Opgenoorth et al.,
tric-ﬁeld component, electron concentration at the heights
1983; Lopez et al., 1991; Hoﬀman et al., 1994).

1360
M. A. Volkov, A. A. Namgaladze: Models of ﬁeld-aligned currents needful to simulate the substorm variations of the electric ﬁeld
Opgenoorth et al. (1983) presented the results of the
Government and No. 95-05-14505 from the Russian Foundation of
observations of the ﬁeld-aligned currents at the western
Fundamental Investigations. The authors would like to thank O. V.
and eastern edges of the auroral surge. The ﬁeld-aligned
Martynenko and A. N. Namgaladze for their assistance in the
calculations and Yu. N. Korenkov and V. V. Klimenko for useful
current ﬂowing out of the ionosphere is connected with
remarks.
the westward-travelling bend of auroras at the western
Topical Editor D. Alcayde´ thanks T. Iijima for his help in
edge of the auroral surge. The speed of the travelling is
evaluating this paper.
about 1—2 km s\ at the ionosphere level. Baumjohann
et al. (1991) presented the satellite observation data of
plasma-sheet variations during the substorm expansion
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